‘-아/어야 해요’ expresses necessity. ‘-아/어야 해요’ is used with adjectives, verbs and ‘-이다/아니다’, ‘있다/없다’. If the last vowel of the stem is ‘아’ or ‘오’, ‘-아야 해요’ is added. If the last vowel of the stem is a vowel other than ‘아’ or ‘오’, ‘-어야 해요’ is added. If the same ends with ‘-하다’, then ‘-하다’ becomes ‘-해야 해요’.

However, while ‘~을(ㄹ) 수 있어요/없어요’ can also be used to express the possibility of doing something, ‘ ~을(ㄹ) 줄 알아요/몰라요’ cannot be.

~을(ㄹ) 줄 알아요/몰라요 expresses whether one knows how or has the ability to do something.
▶ 나는 딸기잼을 만들 줄 몰라요.ⓐI don’t know how to make strawberry jam.

~수(ㄹ) 있어요/없어요 used not only to express the ability to do something but also whether a situation permits somethings to be done.
▶ 나는 딸기잼을 만들 수 없어요.ⓐ I don’t know how to make strawberry jam.
ⓑ I know how to make strawberry jam, but for some reason(such as a lack of strawberries,) I can’t make it right now.